22 June 2012

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Experiment X

Emission Spectrum of 137Cs

Purpose

The purpose of this and the following experiment is to introduce nuclear
measurement techniques, and to investigate some of the properties of nuclear
radiation. For this experiment, the energy spectrum of 137Cs
is measured using a Single Channel Analyzer (SCA).

Introduction

The naturally occurring 133Cs is a stable nucleus. However,
an isotope of cesium, 137Cs, which is a common fragment of the
fission process of 23592U, is unstable due to an excess of
neutrons. This isotope has a half-life of 30.17 years and it decays via
beta- (b-) to 137Ba,
i.e.,

13755Cs ®13756Ba*
+ 0-1e. + n-bar

Often the daughter nucleus, 13756Ba*, is in an excited state and when it decays
to the ground state it emits a gamma-ray (g-ray)
with an energy of 662 keV. (The symbol * indicates that the nucleus is
in the excited state.) In addition to the beta particle, an anti-neutrino,n-bar, is also emitted. However, we will not be concerned with this particle for this experiment.

13756Ba* ®13756Ba
+ g

g-rays are highly energetic electromagnetic
waves. Electromagnetic waves are called photons. The energy of a photon
is given by E = hf = hc/l where h (=6.63×10-34
J·s) is the Planck's constant, f is the frequency of the wave and
l is the wavelength.

The g-ray emitted as a result of 137Cs
decay can induced a number of reactions as it passes through matter.

There
are three types of interactions that the photon can undergo.
1. Compton effect
(Figure 10.1) - In this process, a photon is scattered off from a stationary
electron (or nucleus). The scattered photon loses some energy and thus has a lower frequency than the incident photon.
The amount of energy lost depends on the angle, f.
The higher the angle, the greater the energy lost. If l
is the wavelength of the incident photon, then the wavelength of the scattered
photon is given by

. . . .
. . . . . . . .10.1

where the factor is
called the Compton wavelength and mo is the rest mass of the electron.
When f = 180°,
the photon is back-scattered, i.e., it returns in the direction
it was traveling.

2. Photoelectric effect - A photon may knock an electron completely
out of an atom and in the process it completely disappears. All the energy
of the photon is transferred to the electron.
3. Pair production
(Figure 10.2) - A photon is converted into an electron and a positron.
(A positron has the same rest mass (511 keV) as an electron but has a positive
charge, +e.) In pair production matter in the form of an electron and a
positron is created from pure energy according to Einstein's energy equation,
E = mc2.

When an electron is ejected from an orbit at low energy level, it leaves
behind an empty state. This permits another electron from a higher energy level
to make a transition to the lower level. When this occurs, the electron gives
off an x-ray photon.

For this experiment our objective is to identify as many of the above
processes as possible using a single channel (energy) analyzer. The photons
are detected using a scintillation counter.

The scintillation counter is one of the most commonly used detectors
of g­ and a­radiation.
A NaI crystal containing a small amount of thallium is mounted on a photomultiplier
tube and this assembly is encased in a light tight covering. When a g­ray
or charged particle enters the NaI crystal, collisions with the electrons
in the crystal create excited atomic states near the thallium impurities.
When these excited states decay, a pulse of visible and near ultra­violet
light is emitted from the crystal. The light pulse strikes the "photocathode"
of the photomultiplier tube causing electrons to be emitted by the photoelectric
effect. The electrons from the photocathode are accelerated by an electric
field to a series of plates. At each plate a colliding electron knocks
out several more electrons. The resulting "cascade" is a multiplication
of the electron current. The "gain", or multiplication factor,
of the photomultiplier tube is about 10. The electrical pulse from the
photomultiplier is fed to a Single Channel Analyzer which decides whether
the height of the pulse, i.e., the energy of the original g­
or a­ray, is within the chosen range. If
so, the pulse is further amplified, then fed to a "scaler" which
counts the number of pulses over a set interval of time. It should be noted
that the scintillation system has an overall efficiency of about 5% for
g­rays (meaning that about 5 g­rays
are counted for each 100 striking the NaI crystal). The efficiency depends
upon the energy of the radiation, the size of the crystal,
and other parameters.

Hook up and calibration procedure

NOTE: Make
sure that all power switches are off, and the high voltage (H.V.) controls
are set to zero before you connect or remove the cables.

1. With the power off connect the scaler/timer and the NaI probe to
the (HV connections on the rear panel of the Amplifier/Analyzer using the
signal and High­Voltage cables. (See Figure 10.3).

2. Turn on the scaler and the Analyzer, and set the scaler high voltage
control to 1400 volts.

3. Set the analyzer mode switch to "window" and the baseline­E
(or lower level discriminator LLD) to 65.2% (6.52 turns).

4. Set the window width or DE to 2% and place
the 137Cs source directly under the detector in the near bottom
slot of the holder.

5. Very slowly increase the fine gain control, watching for a
sharp rise and fall in the count rate meter reading. If no such marked
peak of count rate is observed as the fine gain control is increased over
its entire range, increase the coarse gain by one step. Repeat the slow
increase of the fine gain. As soon as the sharp peak in count rate is observed,
adjust the fine gain to the point at which maximum count rate is obtained.

The single channel analyzer is a Pulse Height Analyzer (PHA) for one
channel. The Baseline is a "lower level discriminator" (LLD)
which only passes electrical pulses which are greater that the LLD. With
the mode switch on "Window", the window­DE
control acts as an "upper level discriminator" (ULD). The ULD
stops all pulses with heights greater than the ULD. Thus only pulses with
heights between the LLD and ULD are amplified and counted. On the other
hand if the mode switch is on "integral" all pulses above the
LLD are counted.

As 137Cs has a known g­ray
peak at 662 keV (0.662 MeV), we use this to calibrate the SCA. With the
baseline set to 65.2%, and the "window width" set to 2%, we count
all g­rays with energies between 652 keV
to 672 keV. So we have 1% range = 10 keV, with a full scale calibration
of 1 MeV (1,000 keV = 100%).

Once the calibration as outlined above is completed DO NOT adjust the
gain setting.

6. Turn the computer on and run "Quattro Pro". Load the template
"Energy spectrum.wb3" into memory.

7. Lower the Base-line on the SCA to 0% and count for a 20 second interval.
Record your data on the Quattro Pro spreadsheet. Reset the counter then
raise the Base-line to 2% and repeat the 20 second count. Repeat the count
by raising the Base-line 2% each time until 100% of the analyzer's range
is reached. Don't forget to record your reading for each of the 20 second
interval on your spreadsheet.

8. Follow the on-line instructions and create an xy plot with number
of counts on the ordinate and energy in keV on the abscissa (x-axis).

Analysis

Identify the 32 keV x-ray peak from the 137Ba daughter, the
75 keV x-ray peak from the Pb shield, the Compton scatter region and the 662
keV gamma-ray peak from the 137Cs. Use Figure 10.4 as your guide.

Calculate the full-width-at-half-maximum (FWHM) of the gamma-ray peak
in units of keV. Divide the FWHM by the peak energy (662 keV) and express
as a percentage. Compare your data to Figure 10.4 and comment. (FWHM is
a measure of how well a line is resolved.)

Answer the following questions.

1. Based on the principle of energy conservation would you expect to see pair-production
from the 662 keV g­ray?

2. Explain why there are very few counts for energies greater than 700
keV.

3. Explain why there is a broad range of energy resulting from the Compton
scattering. Use Equation 10.1.